The Portuguese boss felt it was important to bounce back from consecutive league defeats and was buoyed by his side's second clean sheet in the league this term
A Frank Lampard header on the 51st minute was enough for the visitors to secure all three points but they faced a late surge from Steve Kean's men, and the Portuguese manager was delighted with his team's resilience as they bounced back from two consecutive defeats in the league.
"It was important to win the game no matter what and no matter what kind of conditions," said Villas-Boas. "2-0 would be better, we were close to it at the end but couldn't get it and had to suffer a little bit and managed to hold on to a clean sheet.
"Every set play you felt they were dangerous and we managed to be brave enough to defend them.
"It's never easy at Ewood Park, particularly after the moment we were going through with back to back defeats in the Premier League, and also bearing in mind that Blackburn are in desperate need of points.
"It was never going to be an easy game and the difficulties that Arsenal had [in their 4-3 defeat in September] here proved exactly that."
The former Porto coach utilised Daniel Sturridge up front on his own for a league game for the first time and left Fernando Torres on the bench - a decision that the Portuguese boss attributed to the pace of the former Manchester City man.
"We wanted Sturridge up front because we thought that we could make the most of his speed in behind the defenders. Eventually in the second half we decided to put him in the channels and they both [Sturridge and Torres] played very, very well."
Chelsea goalkeeper Petr Cech suffered a suspected broken nose after colliding with Yakubu in the first half but insisted that he wanted to play on, and his manager praised the player's bravery after having suffered from similar incidents in the past.
"He was in tremendous difficulty but Petr's injury prone with these type of incidents, it's not the first time he's had collisions with his head but he gave us good signs straight away after the incident and he felt comfortable," said Villas-Boas.
"We asked him at half time if he wanted to continue and he said yes, which shows the commitment and bravery from the player."
Villas-Boas also reserved praise for Lampard after the midfielder secured the three points with a superb low header, a goal which his manager felt rolled back the years for the midfielder.
"It was a good goal," said the 34-year-old. "I think Frank has found his timing to arrive in the box like the old days. He's scoring a lot in the beginning of this season."